Auction

Question 1

What is the setting in an Independent Private Value Model

Answer 1

n bidders compete for a single unit.

Value of each bidder is private information

All bidders are risk neutral

Question 2

What is a dutch auction

Answer 2

Starts at a very high price and then lowers continously. The first bidder who calls out that she will accept the current price wins the object at the current pirce

Question 3

What is the dutch auction strategically equivalent to ^

Answer 3

Equivalent to the 1st price sealed bid auction

This game is sometimes referred to as an Open 1st price auction

Question 4

What is a 2nd price sealed bid auction

Answer 4

Every player independently chooses a bid, without seeing the other players’ bid and the object is sold to the bidder who makes the highest bid. The price she pays is the second-highest bidders’ bid

In this auction it is optimal for a player to bid her true value whatever other player do

Truth telling is a dominant strategy

Question 5

Prove that truth telling is the dominant strategy equilibrium when having the valuation v

Answer 5

Consider bidding v - x when your true value is v. If the highest bid other than yours is w, then if v-x > w you win the auction and pay w, just as if you bid v. If w>v you lose the option and get nothing just as you would with v. But if v>w>v-x then you lose because you went down without having to

The other way around also possible with the problem of bidding v+x > w > v which means you pay more than you would like to

Question 6

What is an english or japanese auction

Answer 6

Price rises until only one bidder remains. Clearly, it is a dominant strategy to stay in the bidding until the price gets up to your value is reached.

Question 7

What is referred to as an Open 2nd Price Auction

Answer 7

The japanese auction

Question 8

Is Open and Sealed 2nd Price auctions strategically equivalent?

Answer 8

No they’re not because the sets of strategies available to players are different in the two auctions

In an Open, e.g. Japanese auction players see when other bidders quit the auction and could if they wish, condition their behaviour

In the IPV model they do not wish so because they know exactly how much the item is worth

Question 9

Would you condition your behaviour on the information when other bidders would drop out of the auction?

Answer 9

In the IPV model they do not wish to do so because they know exatly how much the item is worth to them, but in a model in which you were unsure of your value and other players had private information about your value, your quitting price would depend on the prices at which other player quit

Question 10

Are the Open and sealed 2nd price auctions equivalent in the

IPV scenario

Common value scenario

Answer 10

First yes, because people do not condition their strategy on what other players do

In the second one no because bidders adjust their bid

Question 11

Is the equilibrium in the second price auctions a dominant strategy or a bayesian nash

Answer 11

Dominant strategy

Question 12

Is the equilibrium in the first price auctions a dominant strategy or a bayesian nash

Answer 12

bayesin nash

Question 13

What does the revenue equivalence theorem say in the IPV case

Answer 13

Assume each of n risk neutral potential buyers of an object has a privately known value independently drawn from the same distribution.

Any auction mechanism in which (i) the object always go to the buyer with the highest value, and (ii) any bidder with the lowest possible value expects zero surplus

yields the same expected revenue

Question 14

Is the Revenue equivalence theorem for the IPV case extendable to the case of K>1

Answer 14

Only if the goods are identical and every bidders just wants one object

Question 15

What could be potentially violated for the RET to fail

Answer 15

Bidders are not symmetric

Not risk neutral

Budget constraints

Bidders valuation is not independent

Bidders can collude

Number is endogenous to the auction design

Question 16

If the RET applies which one is risker, the first price auction or the second price auction

Answer 16

The second-price auction’s revenue is riskier

Question 17

What additional assumption is needed for the RET so all auctions maximise expected revneue

Answer 17

The seller needs a reserve price

Question 18

What are three sealed bid auctions for selling identical units

Answer 18

The discriminatory auction

The uniform price auction

The vickrey auction

Question 19

How do discriminatory auctions work

Answer 19

Each bidder pays an amount equal to the sum of his BIDS that are deemed to be winning

This auction asks each bidder to pay an amount equal to the area under his own demand function

Question 20

How do uniform-price auctions work

Answer 20

In a uniform price auction all k units are sold at a market clearing price such that the total amount demanded is queal to the total amount supplied

Question 21

How can efficiency be achieved if we have that

each bidder demands only one unit

objects are homogenous

Answer 21

Efficiency can be achieved by a simple extension of the second price sealed bid auction

Called the k+1 th price auction (k is the number of units for sale)

Question 22

What type of auction is efficient if we have that bidders have unit demand but objects are heterogenous

Answer 22

A simultanous ascending price auction

In such an auction prices start initially at a low level and bidders express demand by placing a bid on one of the objects.

The prices of those objects that receive more than one bid are raised and the procedure is repeated until demand is equal to supply for each object

Question 23

What type of auction is efficient if bidders demand more than one unit but there are no complementatarities nor substitutability

Answer 23

Efficiency can be achieved by organizing separate one-object ascending auctions

Question 24

What is multi unit demand and following demand reduction

Answer 24

When bidders demand more than one of the objects for sale, distortions can occur that are similar to those in ordinary market with monopsonistic buyers:

bidders can distort their expressed WTP for the marginal unit in order to influence the price of the remaining units

Question 25

What is the exposure problem

Answer 25

Complementarities occur when the value attached to a bundle of objects is higher than the sum of the values attached to the individual objects in the bundle

The exposure problem then occurs when one bidder (who values two goods together higher than the individual components) fears of being stuck with only one good

Question 26

What is the best way to deal with an exposure problem

Answer 26

To allow for combinatorial auctions where agents can place bids directly on entire bundles

Question 27

What happens when we have a multi object auction with complementarities and insufficent flexibility

Answer 27

Leads to inefficiency due to the exposure problem

Question 28

Describe the tension between efficiency and revenue

More specifically, what happens if bidders do not rank objects equally

Answer 28

In multi object setting, even if the situation is symmetric and without complementarities

If bidders do not rank objects in the same order and allowing combinatorial bids while at the same time forbidding bids on signle objects raises the revenue from the auction but at the cost of inefficiently allocating all goods to a single bidder instead of allocating them to different bidders

Question 29

In which auction design is collusion more likely?

Answer 29

The presence of multiple objects for sale creates new possibilities for tacit collusion: firms coordinate their bids instead of competing

The main idea is to share the objects at a low price

Ascending price formats are more vulnerable since they offer reperated opportunities to signal intentials

Question 30

Which auction is less likely to be a victim of tacit collusion

Answer 30

Sealed bid auctions greatly reduce opportunities for signalling, but run the risk of yielding an inefficient allocation

Question 31

To what extent should the design of an auction

depend upon whether the designer’s ojective is ef-

ciency of prot?

Answer 31

Any auction is both ecient and prot maximising in simple symmetric single unit problems. The reserve price may raise prots but lower social eciency. More generally, with a single unit, a rst price auction will be more protable with risk averse bidder, or with asymmetry. The rst price auction will be inecient. The second price auction will be ecient in both cases. With common value components, a second-price auction is especially likely to be mosr ecient, but it needs to be ‘open ascending’. It is worth emphasizing the advantages of ascending auctions in revealing information that is likely to improve the eciency of allocation In practice even in the simplest symmetric single unit settings, rst price auctions are likely to be inecient because bidders do not bid according to the theory, so second price auctions are more ecient

Question 32

Should we always expect a second price sealed bid auction

to have the same outcome as an ascending auction?

Answer 32

If the ascending auction is a japanese auction for a single unit, the auctions are strategically identical if there are just two players - that is, they are “the same game”. So economic theory says that the outcomes will be the same under all circumstances. With private values, a japanese auction OR any other form of ascending auction is identical in Nash Equilibrium outcome, but is not strategically identical, to a second price auction. So if we believe in equilibrium behaviour, they are the same. Believing in nash equilibria simply means believing in rational behaviour. This is because Nash equilibria are in dominant strategies. How- ever, the games looks dierent to ‘non-economist’, so would not necessarily have the same outome in practice. With common value components to val- uations, and more than tow bidders, the games, are dierent - bidders in an ascending auction will learn from, and change their behaviour in response to, others’ bidding. So we should not expect the same outcome.A very good answer mgiht also note than in an ascending auction the winning bidder will not reveal her actual value. In practice, bidders may be unwilling to bid their values in a second-rpcie auction for fear of revealing information that may be useful for others

Question 33

Should we always expect a rst-price sealed bid-auction to

have the same outcome as a descending auction

Answer 33

A rst price sealed auction and a descending auction for a single unit are al- ways strategically identical - that is, they are “the same game”. So economic theory says that the outcomes will be the same under all circumstances. However, the games ‘look di erent’ to non-economists so, in practice, real people may play them di erently, especially since the nash equilibrium is not obvious.